A102531 Real part of absolute Gaussian perfect numbers, in order of increasing magnitude.

3, 15, 6, 19, 111, 91, 159, 72, 472, 904, 2584, 1616, 999, 4328, 702, 4424, 7048, 7328, 2474, 9352, 7144, 7240, 5117, 739, 6327, 15128, 13168, 1263, 14280, 3224, 21704, 15160, 21992, 14044, 23132, 9135, 23656, 24614, 7272, 15464, 9040, 28424, 30956, 14728, 32399

Offset: 1

Author

T. D. Noe, Jan 13 2005

Keywords

• nonn

Comments

An absolute Gaussian perfect number z satisfies abs(sigma(z)-z) = abs(z), where sigma(z) is sum of the divisors of z, as defined by Spira for Gaussian integers.

Examples

			For z=3+7i, we have sigma(z)-z = 7+3i, which has the same magnitude as z.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..76
• R. Spira, The Complex Sum Of Divisors, American Mathematical Monthly, 1961 Vol. 68, pp. 120-124.

Crossrefs

See A102532 for the imaginary part.

Cf. A102506 and A102507 (Gaussian multiperfect numbers). See also A101366, A101367.

Programs

Mathematica

lst={}; nn=1000; Do[z=a+b*I; If[Abs[z]<=nn && Abs[(DivisorSigma[1, z]-z)] == Abs[z], AppendTo[lst, {Abs[z]^2, z}]], {a, nn}, {b, nn}]; Re[Transpose[Sort[lst]][[2]]]

Extensions

a(22)-a(45) from Amiram Eldar, Feb 10 2020